Problem: Reduce to lowest terms: $- \dfrac{5}{3} \div \dfrac{5}{4} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{5}{4}$ is $ \dfrac{4}{5}$ Therefore: $ - \dfrac{5}{3} \div \dfrac{5}{4} = - \dfrac{5}{3} \times \dfrac{4}{5} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{4}{5}} = \dfrac{-5 \times 4}{3 \times 5} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{4}{5}} = \dfrac{-20}{15} $ The numerator and denominator have a common divisor of $5$, so we can simplify: $ \dfrac{-20}{15} = \dfrac{-20 \div 5}{15 \div 5} = -\dfrac{4}{3} $